# ifndef CPPAD_LOCAL_ATAN_OP_HPP
# define CPPAD_LOCAL_ATAN_OP_HPP
/* --------------------------------------------------------------------------
CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-17 Bradley M. Bell

CppAD is distributed under the terms of the
             Eclipse Public License Version 2.0.

This Source Code may also be made available under the following
Secondary License when the conditions for such availability set forth
in the Eclipse Public License, Version 2.0 are satisfied:
      GNU General Public License, Version 2.0 or later.
---------------------------------------------------------------------------- */


namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE
/*!
\file atan_op.hpp
Forward and reverse mode calculations for z = atan(x).
*/


/*!
Forward mode Taylor coefficient for result of op = AtanOp.

The C++ source code corresponding to this operation is
\verbatim
    z = atan(x)
\endverbatim
The auxillary result is
\verbatim
    y = 1 + x * x
\endverbatim
The value of y, and its derivatives, are computed along with the value
and derivatives of z.

\copydetails CppAD::local::forward_unary2_op
*/
template <class Base>
void forward_atan_op(
    size_t p           ,
    size_t q           ,
    size_t i_z         ,
    size_t i_x         ,
    size_t cap_order   ,
    Base*  taylor      )
{
    // check assumptions
    CPPAD_ASSERT_UNKNOWN( NumArg(AtanOp) == 1 );
    CPPAD_ASSERT_UNKNOWN( NumRes(AtanOp) == 2 );
    CPPAD_ASSERT_UNKNOWN( q < cap_order );
    CPPAD_ASSERT_UNKNOWN( p <= q );

    // Taylor coefficients corresponding to argument and result
    Base* x = taylor + i_x * cap_order;
    Base* z = taylor + i_z * cap_order;
    Base* b = z      -       cap_order;  // called y in documentation

    size_t k;
    if( p == 0 )
    {   z[0] = atan( x[0] );
        b[0] = Base(1.0) + x[0] * x[0];
        p++;
    }
    for(size_t j = p; j <= q; j++)
    {
        b[j] = Base(2.0) * x[0] * x[j];
        z[j] = Base(0.0);
        for(k = 1; k < j; k++)
        {   b[j] += x[k] * x[j-k];
            z[j] -= Base(double(k)) * z[k] * b[j-k];
        }
        z[j] /= Base(double(j));
        z[j] += x[j];
        z[j] /= b[0];
    }
}

/*!
Multiple direction Taylor coefficient for op = AtanOp.

The C++ source code corresponding to this operation is
\verbatim
    z = atan(x)
\endverbatim
The auxillary result is
\verbatim
    y = 1 + x * x
\endverbatim
The value of y, and its derivatives, are computed along with the value
and derivatives of z.

\copydetails CppAD::local::forward_unary2_op_dir
*/
template <class Base>
void forward_atan_op_dir(
    size_t q           ,
    size_t r           ,
    size_t i_z         ,
    size_t i_x         ,
    size_t cap_order   ,
    Base*  taylor      )
{
    // check assumptions
    CPPAD_ASSERT_UNKNOWN( NumArg(AtanOp) == 1 );
    CPPAD_ASSERT_UNKNOWN( NumRes(AtanOp) == 2 );
    CPPAD_ASSERT_UNKNOWN( 0 < q );
    CPPAD_ASSERT_UNKNOWN( q < cap_order );

    // Taylor coefficients corresponding to argument and result
    size_t num_taylor_per_var = (cap_order-1) * r + 1;
    Base* x = taylor + i_x * num_taylor_per_var;
    Base* z = taylor + i_z * num_taylor_per_var;
    Base* b = z      -       num_taylor_per_var; // called y in documentation

    size_t m = (q-1) * r + 1;
    for(size_t ell = 0; ell < r; ell++)
    {   b[m+ell] = Base(2.0) * x[m+ell] * x[0];
        z[m+ell] = Base(double(q)) * x[m+ell];
        for(size_t k = 1; k < q; k++)
        {   b[m+ell] += x[(k-1)*r+1+ell] * x[(q-k-1)*r+1+ell];
            z[m+ell] -= Base(double(k)) * z[(k-1)*r+1+ell] * b[(q-k-1)*r+1+ell];
        }
        z[m+ell] /= ( Base(double(q)) * b[0] );
    }
}

/*!
Zero order forward mode Taylor coefficient for result of op = AtanOp.

The C++ source code corresponding to this operation is
\verbatim
    z = atan(x)
\endverbatim
The auxillary result is
\verbatim
    y = 1 + x * x
\endverbatim
The value of y is computed along with the value of z.

\copydetails CppAD::local::forward_unary2_op_0
*/
template <class Base>
void forward_atan_op_0(
    size_t i_z         ,
    size_t i_x         ,
    size_t cap_order   ,
    Base*  taylor      )
{
    // check assumptions
    CPPAD_ASSERT_UNKNOWN( NumArg(AtanOp) == 1 );
    CPPAD_ASSERT_UNKNOWN( NumRes(AtanOp) == 2 );
    CPPAD_ASSERT_UNKNOWN( 0 < cap_order );

    // Taylor coefficients corresponding to argument and result
    Base* x = taylor + i_x * cap_order;
    Base* z = taylor + i_z * cap_order;
    Base* b = z      -       cap_order; // called y in documentation

    z[0] = atan( x[0] );
    b[0] = Base(1.0) + x[0] * x[0];
}
/*!
Reverse mode partial derivatives for result of op = AtanOp.

The C++ source code corresponding to this operation is
\verbatim
    z = atan(x)
\endverbatim
The auxillary result is
\verbatim
    y = 1 + x * x
\endverbatim
The value of y is computed along with the value of z.

\copydetails CppAD::local::reverse_unary2_op
*/

template <class Base>
void reverse_atan_op(
    size_t      d            ,
    size_t      i_z          ,
    size_t      i_x          ,
    size_t      cap_order    ,
    const Base* taylor       ,
    size_t      nc_partial   ,
    Base*       partial      )
{
    // check assumptions
    CPPAD_ASSERT_UNKNOWN( NumArg(AtanOp) == 1 );
    CPPAD_ASSERT_UNKNOWN( NumRes(AtanOp) == 2 );
    CPPAD_ASSERT_UNKNOWN( d < cap_order );
    CPPAD_ASSERT_UNKNOWN( d < nc_partial );

    // Taylor coefficients and partials corresponding to argument
    const Base* x  = taylor  + i_x * cap_order;
    Base* px       = partial + i_x * nc_partial;

    // Taylor coefficients and partials corresponding to first result
    const Base* z  = taylor  + i_z * cap_order;
    Base* pz       = partial + i_z * nc_partial;

    // Taylor coefficients and partials corresponding to auxillary result
    const Base* b  = z  - cap_order; // called y in documentation
    Base* pb       = pz - nc_partial;

    Base inv_b0 = Base(1.0) / b[0];

    // number of indices to access
    size_t j = d;
    size_t k;
    while(j)
    {   // scale partials w.r.t z[j] and b[j]
        pz[j]  = azmul(pz[j], inv_b0);
        pb[j] *= Base(2.0);

        pb[0] -= azmul(pz[j], z[j]);
        px[j] += pz[j] + azmul(pb[j], x[0]);
        px[0] += azmul(pb[j], x[j]);

        // more scaling of partials w.r.t z[j]
        pz[j] /= Base(double(j));

        for(k = 1; k < j; k++)
        {   pb[j-k] -= Base(double(k)) * azmul(pz[j], z[k]);
            pz[k]   -= Base(double(k)) * azmul(pz[j], b[j-k]);
            px[k]   += azmul(pb[j], x[j-k]);
        }
        --j;
    }
    px[0] += azmul(pz[0], inv_b0) + Base(2.0) * azmul(pb[0], x[0]);
}

} } // END_CPPAD_LOCAL_NAMESPACE
# endif
